How am I supposed to move only Gizmo when in Edit mode?
Exactly... You can easily solve this using the 3d cursor...

First be sure that you set the pivot point to the 3d cursor (in object mode): 



Back in edit mode you select the edge where you want the center of rotation and hit Shift+S to set the 3d cursor to that edge: 



Problem solved, if your cursor is at the right place you can rotate everything around that point: